On the Diameter, Girth and Coloring of the Strong Zero‑Divisor Graph of Near‑rings
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In this paper, we study a In this paper, we study a directed simple graph $\Gamma_{s}(N)$ for a near-ring $N$, where the set $V^{*}(N)$ of vertices is the set of all left $N$-subsets of $N$ with nonzero left annihilators and for any two distinct vertices $I,J\in V^{*}(N)$, $I$ is adjacent to $J$ if and only if $IJ=0$. Here, we deal with the diameter, girth and coloring of the graph $\Gamma_{s}(N)$. Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring $N$ in the left annihilator of some vertex in the strong zero-divisor graph $\Gamma_{s}(N)$.
Abstract
In this paper, we study a directed simple graph $\Gamma_{s}(N)$ for a near-ring $N$, where the set $V^{*}(N)$ of vertices is the set of all left $N$-subsets of $N$ with nonzero left annihilators and for any two distinct vertices $I,J\in V^{*}(N)$, $I$ is adjacent to $J$ if and only if $IJ=0$. Here, we deal with the diameter, girth and coloring of the graph $\Gamma_{s}(N)$. Moreover, we prove a sufficient condition for occurrence of a regular element of the near-ring $N$ in the left annihilator of some vertex in the strong zero-divisor graph $\Gamma_{s}(N)$.
참고문헌 (12)
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